Norm index formula for the Tate kernels and applications

摘要

Let p be an odd prime and L/F a p-extension of number fields with Galois group G. The aim of this paper is to provide answers to a question of Kahn concerning lower bounds for the order of the kernel and cokernel of the functorial map K2F → K2L ~G. To this end, we first determine a norm index formula for generalized Tate kernels and then express our lower bounds in terms of the ramification in L/F.